Geodesic
Leibniz Algebras, Lie Racks, and Digroups
Journal of Lie theory, Tome 17 (2007) no. 1, pp. 99-114.

Voir la notice de l'article provenant de la source Heldermann Verlag

The "coquecigrue" problem for Leibniz algebras is that of finding an appropriate generalization of Lie's third theorem, that is, of finding a generalization of the notion of group such that Leibniz algebras are the corresponding tangent algebra structures. The difficulty is determining exactly what properties this generalization should have. Here we show that Lie racks, smooth left distributive structures, have Leibniz algebra structures on their tangent spaces at certain distinguished points. One way of producing racks is by conjugation in digroups, a generalization of group which is essentially due to Loday. Using semigroup theory, we show that every digroup is a product of a group and a trivial digroup.
Classification : 17A32, 20M99, 22A30
Mots-clés : Leibniz algebra, Lie rack, digroup 
@article{JLT_2007_17_1_JLT_2007_17_1_a6,
     author = {M. K. Kinyon },
     title = {Leibniz {Algebras,} {Lie} {Racks,} and {Digroups}},
     journal = {Journal of Lie theory},
     pages = {99--114},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2007},
     url = {http://geodesic.mathdoc.fr/item/JLT_2007_17_1_JLT_2007_17_1_a6/}
}
TY  - JOUR
AU  - M. K. Kinyon 
TI  - Leibniz Algebras, Lie Racks, and Digroups
JO  - Journal of Lie theory
PY  - 2007
SP  - 99
EP  - 114
VL  - 17
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JLT_2007_17_1_JLT_2007_17_1_a6/
ID  - JLT_2007_17_1_JLT_2007_17_1_a6
ER  - 
%0 Journal Article
%A M. K. Kinyon 
%T Leibniz Algebras, Lie Racks, and Digroups
%J Journal of Lie theory
%D 2007
%P 99-114
%V 17
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JLT_2007_17_1_JLT_2007_17_1_a6/
%F JLT_2007_17_1_JLT_2007_17_1_a6
M. K. Kinyon . Leibniz Algebras, Lie Racks, and Digroups. Journal of Lie theory, Tome 17 (2007) no. 1, pp. 99-114. http://geodesic.mathdoc.fr/item/JLT_2007_17_1_JLT_2007_17_1_a6/